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The standard narrative around the student loan "crisis" holds that college has become unaffordable for most students without accumulating massive amounts of debt, and that the problem has gotten worse in recent years.

But new federal data released today show that the overall rate of student borrowing was lower in the 2015-16 academic year than it was four years prior -- the last time such a comprehensive study was released -- even as the average federal loan amount rose slightly among those who borrowed.

According to the National Postsecondary Student Aid Study, a quadrennial survey of undergraduate and graduate students enrolled in college in a given year, 38 percent of undergraduates took out student loans in 2015-16, down from 42 percent in 2011-12. And the proportion of students borrowing was lower for almost every institution type -- community colleges, four-year public institutions, private colleges and for-profit colleges.

Borrowing rates were also down among both full-time and part-time students.

Two- and four-year for-profit programs saw some of the biggest drops in the proportion of students borrowing. For-profit colleges have been at the center of an ongoing battle over Obama-era regulations to rein in poor-quality programs that graduate students with debt they can't repay, and to provide relief on loan repayment to students defrauded by their institutions. The Department of Education and Secretary Betsy DeVos are in the midst of a rewrite of those rules to take into account complaints from institutions.

Students who borrowed to attend those programs, however, took out significantly more in total student loans. At two-year for-profit programs, the average total student loan amount jumped more than 16 percent, from $7,200 in 2011-2012 to $8,400. At two-year community colleges, meanwhile, the average total loan amount remained unchanged at $4,700.

Among all undergraduates, those who borrowed took out an average of $7,600 in loans, an increase of $500 over the previous data.

It's not clear what may be behind the lower overall borrowing rates. The proportion of students receiving federal Pell Grants also dropped between 2011 and 2015, although the average value of the grant did increase by $300. And while the proportion of students receiving state grant aid appeared to jump significantly, that may reflect a change in how the National Center for Education Statistics counts Cal Grants as much as it does higher participation in those programs.

But average overall grant amounts -- including federal, state and campus-based sources -- rose from $6,200 to $7,600.

That growth in grant aid reflects recent upward trends in state-funded aid. Although that growth leveled out in 2015-16, total awards of need-based aid jumped sharply in recent years, according to the National Association of State Student Grant and Aid Programs.

Policy decisions by the Obama administration may have played a role in making state aid more generous. The 2009 stimulus package injected tens of billions of student aid into the higher ed system (in the first year after the stimulus, total expenditures on the Pell Grant program shot up from $20 billion to $33.5 billion). And the administration and Democrats in Congress insisted that the law include measures requiring states to maintain their own education spending to qualify for the additional federal funds.

And as the job market has picked up since the Great Recession, the annual enrollment of students in higher ed institutions has declined continuously -- possibly meaning fewer students who seek out aid via grants or loans.

The data suggested that for graduate students in particular, the aid picture has become even tighter. The percent of graduate students getting teaching assistantships declined from 12 percent to 8 percent, and the average value of those assistantships fell more than 8 percent, to $13,400. Meanwhile, the proportion of graduate students taking out federal Grad PLUS loans remained flat at 10 percent, but the average loan amount jumped nearly 20 percent, to $22,300.

Students taking out Grad PLUS loans can borrow an unlimited amount up to the cost of attendance for their program. But the PROSPER Act, House Republicans' version of a Higher Ed Act reauthorization, would cap those graduate loans at $28,500 annually.